I have done a similar distance but it took a while to build up and seldom did this daily, going by train or staying in Drs' accommodation when this suited me better.
Can you be more specific about your struggle?
Is the whole trip a battle or do you get empty legs part way through?
Hmmm, had to think about this and breaks it down to the fact that it maybe not that much physical:
1. I can't deny is the stop/ start and the sheer number of cars I have to deal with on the way home. I not so bothered on the way in, as its seems to flow a lot more and I leave at as early as I can so do miss some traffic.
2. Physically about 12 miles in, I just feel tired as its a big push to get through the next 4 miles, the last mile or so is easy as I am pretty much there
3. Its tough in the wind, as I go west and its generally blowing a westerly
4. It never gets easier - I have to keep pushing and even then I am not really any quicker and its still taken me about 1.5 hours or more.
5. I think there is also some expectation management in that, even after 3 years or so, its still hard, its not like I can jump on the bike and simply go (well I can, but at no part of the ride do I feel this is easy)
I do have a couple of different routes I try that minimise my time in traffic but the slog out of Central London is just that a slog.