First of all, congratulations on the offers!
We live in the Southfields Grid (so assume very close to you). We have a very happy daughter at WHS (Y9) but it was not necessarily her top school when doing the 11+. When she got the offers we said that she will decide but that we wanted her to do the commute in "normal" conditions when attending the offer holders events, so she could see the difference it made. She came to the conclusion, on her own, that being close by was a massive plus, especially when the difference is so marked (like in your case with LEH, we are taking more than half an hour of extra commute each way, so an extra hour per day).
Plus, the fact that the commute to WHS can be done by different means so you are not dependent on the traffic / road blocs, etc.
Our DD came to realise herself and now is the first one to joke about how some of the early starts would be been so much harder if she had chosen another option.
Also worth noting that, beyond the fact that it is an extra hour per day everyday for 7 years, being that much closer also makes a massive difference in terms parents engagements, clubs and activities before and after school and, crucially, meeting friends outside school (who are likely to be both closer by and also more used to travel on their own on public transport).
Good luck and feel free to pm me if you have any questions.