MFP doesn't seem to be working

As always some good (and some bad) advice here.
I'd definitely say to find and or make the time to weigh food correctly and estimate correctly. As you say you may be over-estimating what you're eating (and the food nutrition database may be inaccurate due to being user generated) I'd advise you look closely at these areas. You may be eating under what you need.
In addition I can't recommend enough monitoring your sodium at this stage, and making sure you're hitting your full 8 cups of water (2 litres over here) at least every day.
Try to be more active - I know it's real hard at first and with the job you have, but you will feel better for it .This journey's for your health and well being, not the scales. So make time for yourself over your job and so on.
ETA: - And yes MFP may be overestimating your calorie burns. If you can't afford a HRM try comparing to other sites' estimates and manually adapt it - type cals burned into the box. -
And yes, do also take your measurements. There are online guides to help if you're still not sure what you're doing here.
Also be patient. Starting off your body's not sure what's happening, and it takes a long while to get it accustomed to the changes you've made. You've got this!

you haven't even given it a week. our body weight changes daily, so always try and weigh in on the same day

As body weight fluctuates so much, wouldn't making measurements more often increase the resolution of data and, hence, improve the reliability of any trends that are identified? I just have my physics hat on

No, body weight fluctuates due to water weight, and all other sorts of different things. for example- a few years ago i weighed in on a wednesday- and then weighed on the sunday, and was 5lb heavier on the sunday, but when it got back to the wednesday again, i had actually lost 3lb to the previous week. every day is different, which is why so many people say weigh the same day and same time. its more reliable to weigh the same day and time as its more reliable- like keeping a control in an experiment- if we have to go down the scientific route.

I use a phone app called "Libra" that does a weighted moving average calculation to plot weight trends, so I weigh daily and plug the numbers into that.

I always wonder if these calorie estimates from gadgets, apps and gym machines are gross or net - do they take account of the fact that you would have been using 50 - 80 calories an hour lying down ? So is 240 calories burned in an hour 240 extra or (240 - RMR) ?

1. How are you weighing yourself? I weigh myself on Sat. after I do 1 and 2. Pants belt and keys weigh a lot. You have to be consistent in the beginning on you weigh-ins.
2. What is your sodium intake looking like? Make sure you rinse your tuna and if you buy can goods get the veggies that are in water.
3.What type of Cardio are you doing? Personal I've had more success with taking a walk around the block than any crazy workout video or a gym membership.

A couple of things:

You asked about sodium: Salt encourages the body to retain water - cut the salt, lose the water! And you be amazed how much that water weighs! Don't cut it out completely though, the body needs a little to operate efficiently.

You set your activity level as sedentary. Have you tried upping the level - you are at least "lightly active" - and not adding back the calories for your normal daily movements? Try to do some additional exercise where you can, and add those calories back.

I say at least lightly active - I used to be a high school librarian and walked huge distances some days, just in the normal nature of my job - from the library to the staff room and back was a quarter of a mile and I did that at least four times each day. When I was required to cover classes in our physics block that was at least as far again! I would often run errands round the school myself, rather than sending a student. My pedometer some days clocked up 25000 steps!

You also said you were (over-)estimating calories consumed at lunchtime. Unless you are lucky enough to get lunch at school for free (I never did!), would it make more sense to take a packed lunch? Then you know exactly what's in it and can accurately assess the calories: A sandwich, a salad, and several pieces of fruit (the occasional packet of crisps or a biscuit, too, if you really want) should keep you going!

The only sure-fire way to lose weight (and keep it off) is to eat less and move more, but getting the balance right between eating and moving can take several weeks to perfect. Keep trying - you will achieve!!

ok, ill put it another way. when you weighed in a few days after your orignal weigh in, tell us what you were honestly expecting to see the scales to show? a few lbs? please be honest

For the last few days it has given me a figure of about 350calories, which increases my calorie intake limit to about 2350; marginly less than the 2500 calorie RDA for males.

Don't forget the figure you see on MFP already includes a deficit, you said you want to loose 2lb per week so MFP will have already deducted 1000 cals per day from your TDEE (Total Daily Energy Expenditure). TDEE is BMR * activity level (1.2 for sedentary). 2500 recommended is averaged over all men, as a tall guy with some weight to loose, yours will be somewhat higher than that. Best to leave it as is for now and see what happens over a whole week, two weeks, month. If after a month your weight isn't dropping, then maybe adjust your target cals a bit and see what happens.

You may be eating under what you need.

In which case, I would expect lose weight faster.

Logically yes. In reality, perhaps not. This is a highly contentious topic; lurk more on the forum and you'll learn. I can only attest to my own experience for sure, and I've found by increasing my calories; including net, I've dropped more. The body is like a machine, it needs fuel to function best. That analogy works for me.

In addition I can't recommend enough monitoring your sodium at this stage

I'm not usually so bad with salt, but I'm curious about the link between salt and weight loss. I understand the health benefits of cutting out salt, but I cannot see how a reduction in salt will help me lose weight. I am not saying you are wrong, certainly not! I am just curious about what the link is (please don't think I am being dismissive).

Could be broscience but again I've found that my body stores extra weight 'water weight' on a higher sodium intake.

True. I'm just trying to postpone death by a few more years before the inevitable shadow hands of fate grasp me in the night and drag me to the abyss of oblivion, whereupon my very essence of being will cease to exist and all perception of the joys and pains of this world will hault forever.

Touché.

Added you as a friend. I also teach (as part of my PhD) so I have some understanding of the difficulties of your work and it's impact on your lifestyle. We also have in common the fact that I, one day apparently will die.