Can anyone recommend a cheap grass strimmer? I only have a small area of
lawn.

I've a Flymo Mini - strim which I use to strim the edges of my small lawn.
it seems fine but you have to buy individual little "lines" to put in it
(i.e. the bits that cut) and they seem to wear out quickly so it works out
expensive. I think I'll buy one where you can get reels of wire to cut
yourself next time.

If you actually want to cut the whole lawn I'd be careful using a strimmer -
we had a v small lawn in an old house and "killed" quite a hefty strimmer by
using it to cut the whole lawn - I don't think that the motors are really
designed for "grass cutting", just for "edge strimming".
Hayley