Tours to London - best option?

If you're not hauling too much luggage it might be easier,quicker, and cheaper to fly. Ryanair flies from Tours airport to London Stanstead. I found flights in June as low as $51. You could get a taxi to the airport in Tours and then take the train from Stanstead to London. That would add some $$ but it still might be cheaper than the Eurostar. At least worth looking into.

Are you transporting your bikes? I guess not, or you could ride them from one station to another :-)

Trains from Tours go into Paris Montparnasse, Eurostar trains to London leave from Paris Nord. Can you take your luggage on the métro? If yes, OK, if no as 4 people taking a taxi would not be too expensive per person.
Yes, changing at Lille would be a lot easier, but there are two stations in Lille. Eurostar uses Lille Europe, the other station is Lille Flanders. I can see at least one option from Tours that uses Lille Europe:

Train N 8264, depart Tours 11:47, arrive St-Pierre-des-Corps 11:52
Train TGV 5264. depart St-Pierre-des-Corps 12:00, arrive Lille Europe 14:30
Train EST 9141, depart Lille Europe Eurostar 15:36, arrive London St. Pancras International 16:05

Sounds perfect. There is also an earlier (09:49) departure which requires an extra change at "Aeroport Paris-Charles de Gaulle TGV".

I would say wait until you can book it all as one transaction, that way you will not get caught if things change.
I would recomend https://loco2.com/ they allow booking 3 months out, and will do a through booking Tours - London. For dates in May, they are currently offering the abovementioned 11:47 train for £88 Tours to London.

Thanks, that sounds like a good plan, but I'm concerned about the eight minute time to change trains at St. Piere des Corps. Do you think that might be a problem?

Changing trains in Lille is certainly easier than in Paris (where you have to cross town to change stations). St. Pierre des Corps is small, so that transfer time doesn't worry me either, but do be prepared to jump right off the train and not dawdle. French trains can usually be booked 3 months ahead; Rail Europe has the St. Pierre to Lille leg for sale for June 3, for instance, for $31. You can add multiple tickets into one shopping cart, but it is often better to enter each leg separately; RE's cart can't really deal with more than one connection. For this example, breaking up the pieces was also cheaper ($31 + $11 vs a quote of $65 to book "one ticket" from Tours to Lille).

As always with RailEurope, shop around for price comparisons. Remember, it is a ticket seller, not an operator.
You can buy a ticket (as soon as possible) on the SNCF site, http://en.voyages-sncf.com/en/ for this itinerary June 3: Depart at 1:47 p.m. on the Tours navette to St-Pierre, connecting through Lille to St-Pancras, for around $61 US (I'm converting from euros.)
The same schedule being sold by RailEurope is around $115. Assembling individual legs on RE might save $15 or so.
Other itineraries through RailEurope, requiring the awkward connection in Paris via Montparnasse or even Austerlitz to Gare du Nord, begin at about $73. Traversing Gare du Nord itself is not one of life's more relaxing exertions.
It's worth noting that the connection from the centre of Tours to St-Pierre, just outside town, is scheduled to take five minutes, either a local train or bus, with departures every 15 to 30 minutes. If you want to set your own pace, buy St-Pierre-St-Pancras now and pick up the local ticket there. Price from SNCF: $1.53. Price from RailEurope bought separately in advance: $11.