Neil, you can get ANY train from Gatwick into london. The Gatwick Express is just the fastest (non stop) and most expensive. It also only arrives to Victoria station in west London. Other train companies that operate are

Southern: to Victoria, stopping on the way at East Croydon and Clapham Junction
First Capital Connect (FCC): to London bridge, Waterloo, Blackfriars, Faringdon or St Pancras/Kings Cross with only ONE stop at East Croydon

These trains are just as frequent as the Gatwick express

The FCC service is about GBP2.40 cheaper than the Southern service and you can buy a ticket that's valid for that train only. If you want to go by Southern you need to buy the more expensive ticket valid for ANY PERMITTED ROUTE which allows you on both southern and FCC (but not gatwick express)

fares are:
gatwick Express: 16.90
Southern or FCC: 11.30
FCC Only : 8.90

So, go by FCC!