Yes, they do it by detecting the IF frequencies. Or at least they claim to, because I haven't seen a TV detector van since the 1980s. If you used an IF transmitter then they would prosecute you for having an licensed transmitter, which would probably be a heftier fine than that for having a TV. The antennas they use/used were directional anyway, so you couldn't flood an area. They are really nasty people sometimes, and will pester you over and over and over again, with all sorts of nasty threats about court, fines, and the rest, despite having no evidence. A friend of mine who used his TV purely for watching DVDs and playing console games ended up taking legal action against them to get them to desist from their threats.
People outside the UK seem to think that all UK TV is BBC. This hasn't been the case since 1955! Looking at my TV with digital terrestrial adaptor, I currently have:
BBC 1, BBC 2, BBC 3, BBC 4, CBBC, CBeebies, BBC News, BBC Parliament + 2 Interactive channels
Then the independents:
ITV1, ITV2, ITV 3, ITV4
Channel 4, 4+1, More 4, E4, E4+1, Film 4, 4 Music (Also run with state aid but independent of the BBC)
FIVE, Fiver, Five USA
Sky Three, Sky News
Yesterday
QVC
G.O.L.D. (pay)
Dave an Dave Ja Vu (+1) (Mainly Top Gear and panel game repeats)
channel One
VIVA
Quest
Ideal World, Bid.TV, Home, Big Deal, Create and Craft, Price drop TV, Rocks and Co, Gems TV
ESPN (pay)
CNN
Sky Sports 1 , Sky Sports 2 (pay)
10 or so "Adult" pay channels
Topup1/2/3 (pay)
Thats on terrestrial standard definition alone, there are a few terrestrial HD channels, and umpty million more on Sky (satellite)