Working out calorie limit - BMR vs. MFP

1lb a week might be too agressive number 1.
If you have 75+ lbs to lose 2 lbs/week is ideal
If you have 40-75 lbs to lose 1.5 lbs/week is ideal
If you have 25-40 lbs to lose 1 lbs/week is ideal
If you have 15 -25 lbs to lose 0.5 to 1.0 lbs/week is ideal
If you have less than 15 lbs to lose 0.5 lbs/week is ideal

IIFYM.com includes exercise calories...MFP does not...if you do exercise you eat back those calories...

you are comparing apples to oranges in this case...

If TDEE is 2286, then 2286-500 = 1786. Pretty close to MFP. Not sure how you got 2050 from TDEE of 2286?

I'm currently about 90kg, 188cm tall, 35 years old and ideally looking to lose about half a kilo per week (one pound) to achieve a target weight of around 80kg.

If I plug those numbers into the MFP app, setting my lifestlye as sedentary (which it is - desk job with driving), it gives me a target of 1820 calories per day. I'm having no trouble at all sticking to that (in fact I occasionally have to make myself eat more to meet it).

Recognizing that half a kilo is about 1.1 lb, this means that MFP has your NEAT (TDEE minus exercise) at 2370.

However if I calculate my BMR and TDEE using this site: http://iifym.com/tdee-calculator/ , it suggests that I need 1905 minimum calories, and that my TDEE is 2286. So going by recommendations from elsewhere on the web, I reckon from those numbers that I need to aim for about 2050 calories per day to lose weight.

Couple things -- first, your BMR is an estimate. You are going to get a variety of numbers depending on the calculator you use. So MFP's number and your BMR are kind of close, even though the MFP method uses BMR only to calculate NEAT and it has nothing really to do with the final goal set. Plus, there's no particular reason that you can't eat a little below your BMR, especially if you really are sedentary/don't exercise, so based on this the MFP number seems fine, especially since you should eat back exercise calories/

More significantly, there's an error here. If your TDEE is 2286, that means you need to subtract 550 calories per day to get a 1.1 lb loss, giving you a 1736 calorie goal. That's lower than what even MFP said.

Your calculation is not based on the calories/week needed to lose any particular amount, but on taking off 10%, or about 229. That's a fine way to do it, and you should lose weight if the rest of your inputs are correct, your metabolism is at least average for your size, you log correctly given the smaller margin of error, etc. But a deduction of 229 without increasing exercise isn't supposed to give you a loss of half a kilo a week, which is the target you requested from MFP, but instead slightly under half a lb a week (half a pound requiring a deficit of 250 calories per day).

So it looks to me like there's no inconsistency here of any significance. The question is what's a reasonable target loss per week and deficit given your current stats. If my math is right as to your stats, half a lb (or a quarter of a kg, if that's how MFP has it for you) is probably more reasonable than half a kg, but that's up to you. If you adjusted MFP, the results would probably be similar to your TDEE without exercise calculation.

TL/DR version of the last post--

There seems to be a wide belief that TDEE minus 10% is about a pound loss per week and TDEE minus 20% about 2 lbs, although sometimes I see the latter described as 1 lb. But of course since these are percentages it depends on your starting TDEE. If your TDEE is low or calculated without adding the exercise that you do, even 20% could be less than a lb/week. If I did not exercise, 20% of my TDEE would calculate to barely over 0.5 lb/week.