I have been told that is you upgrade your wheels and tyres from 15 inch to 16 inch, your speedo doesn't change, is that true?

I went from 205/65R15 to 225/560R16 wheels and tyres.

Also, when I apply the brakes, the car shudders a little, am I due for a brake adjustment?

You can check the wheel change with a rolling
radius calculation...
to calculate a 205/65/15....
(205mm x 65%) + 190.5mm
(the 190.5 figure is 7.5", or half your wheel, x 2.54mm, thus
inches to mm conversion)

Do the same with the 16" setup and if your pretty close,
you are OK.

Clear as mud??

There is a calculator page here somewhere on Fordmods,
but I cant seem to find it.

Brake shudder may be warped rotors. I get it sometimes, but
it seems to go away as well.