Is there a cheaper/slower alternative to Eurostar between Lille and London?
No. To go between France and the UK by train, you need to cross the Channel Tunnel. Only three types of trains cross the Channel tunnel:
The Tunnel will soon open to competition, but the other competitors are likely to be high-speed trains heading to other locations, with similar prices.
I think the cheapest way of crossing the tunnel is with a bicycle, if you have one. It may not be as cheap if you need to rent a bicycle or to buy one in Lille and sell it off in London or if you factor in the expenses along the way.
You can also investigate ferry crossings. Since the train is faster and more comfortable, ferries can but compete on price.
You can use a combination of "classical" trains and ferry.
A detailed description with up-to date information is available here: http://www.seat61.com/London-Paris-ferry.htm
This option is only cheaper if you book on shorter notice. If the Eurostar is booked in advance it will be cheaper.
If you have a vehicle, you can use the Eurotunnel Le Shuttle.
Passenger vehicles are carried in a car shuttle train, made up of closed wagons. You can get out and walk along inside, and there are bathrooms, but otherwise it's fairly basic.