Hi Bethy! A machine for around £100 will not be a professional one. It will be for light, home use. I would not recommend going for such a machine if you want to do spray tanning professionally.
Earlex machines (including MaxiMists - the full MaxiMist, not the MaxiMist Lite) are generally considered #1 in the UK, so you won't go wrong with an Earlex TS20, TS50, or full MaxiMist.
The TS20 is good for moderate use (up to ten tans per day), and the TS50 and MaxiMist are both good for heavy use.
You may find it a lot more cost-effective to purchase a
spray tan starter kit, which will include everything you need to get going: machine, tent, solution, and possibly some consumables too. There are loads out there so just take a look, compare them and pick the best one for you.
Bear in mind most websites aimed at professionals will show pricing before VAT (though they should mention in the description that this is the case), so remember to account for that