I went to TPS to go get a new MAF sensor and the part that they quoted me for was an air mass meter for £85. Is the air mass meter just the whole unit with the sensor already fitted in it?

Yes and normally they would ask for your old one back so it can re built to new standard. Well that's what my local dealer asked for.

As mentioned it's the whole unit. I got my Bosch recon from a motorfactor for £65 all in