Jon -- I do understand what you're trying to do, and in one sense applaud you -- life on the road is hugely easier when you don't have to check in to a new hotel every bloody night. But the guys are right in a lot of what they say. Principally, you really do need to factor traffic into your planning. Google says Heathrow to Lytham is four hours and five minutes, and if the road is clear, I generally beat Google by a good amount of time. But you could literally get a jam anywhere between Heathrow and Preston, and it only needs one decent queue on the motorway to leave you racing to get to Lytham for your tee time, with your only nourishment post a redeye flight a chocolate bar grabbed in the pro shop.
Once ensconced in your hotel in Twickenham, you are at the mercy of the M3 and the M25 every morning and evening. Now, you _should_ be going against most of the traffic -- you will be heading out of town in the morning when the commuters are coming in, and back in the evening when they're heading home. But all bets are off once you hit the M25 and London's main roads are busy enough that they can stuff up anywhere, at any time.
It could, might, should even work out fine. But the south east of England is not rural Scotland. Yes we have better roads but they are cramful for a large part of the day. If you were doing an LA area trip, how long would you allow for a thirty mile journey in the morning rush hour that was mostly up 405? Those are the sort of questions you should be asking yourself for this trip.