As has been said, you are entitled to 75% of the downgraded sector (not including taxes but including surcharges) under EU regulations.

Work out the percentage of the distance of the downgraded sector, and use this to calculate how much you should be refunded.

There are some examples on the EC261 thread on the BA forum.

ETA :- Now that I'm back on a proper computer...

MAN-DXB = 3518 miles
DXB-BKK- 3050 miles

So, the return is 13135 miles.

The DXB-BKK leg is 23.2% of the total.

Let's say the F return is £5000 not including government taxes.

23.2% of £5000 = £1160

So, under EC261 you'd be entitled to 75% of £1160 = £870

*I think