It depends on many things.
The BAA's attitude is that plane spotters are not wanted. They get a number of calls per day about photogs/spotters, and always pass them to Police.
Once that happens unless you fall into one of the 3 catagorys for being on the airport, which spotting isn't one of, usually you'll be asked to move. If you arn't, sure as eggs are eggs, Police will get called back again within 30 minutes.
Obviously Police have the powers to ask you to go anyway, irrespective of the BAA calling them or not. It then depends on the Police Officer, some will always move on, others will ask you to disappear to somewhere less obvious. However, the number of photogs/spotters who take the micky soon make the second of those 2 groups of officers change to always applying number one option.
Unfortunatly not all who spot and take photos are paragans of vertue, irrespective of what some may think, and at the end of the day, it's private property and you have no right to be there.