London Hotel Transfer

Three of us (inluding my 9 year old daughter) will be traveling to London in July. Given that we'll have ten days worth of luggage, what would you recommend for transportation into central London (Mariott County Hall) from Heathrow on a Sunday? It would appear that the London Express would run around 40 GBP for three, a taxi 40-50 GBP and a limo around 165 GBP! What's the best price/performance and least hassle-factor? Thanks in advance!
Steve
Steve