Kabbee is an app/website that allows you to search the best deal from hundreds of minicab companies in London. I also have a promo code that will get you £10 off your first order (this is guaranteed to work).
Considering the promo code and the fact that you get to choose the best price from quite a few cab companies you might find that it will be pretty much the same price as the train/coach+tube transfer and you will also travel in style.
How to use kabbee vouchers
If you want to have a use the voucher and please visit the Kabbee website here and when you sign up add the code: K9C3CQ to your account to get £10 off your first cab journey.