You have not spent much time in Welly then !!
Yes, I'm booked on the return train - as long as I don't miss it. Again, I am expecting the reservation system to be honored. To be honest you don't see many people travelling with bikes on the train, it will be interesting to see how this changes in the summer.Can you get your bike on the return train OK?
Can you manage the commute with 2 bikes? Solid tyres are probably a good choice for any bike you leave in London.
A 10 mile morning ride can be done in polycotton pants, the Go Outdoors ones are cheap, quick-dry and narrower cut than most.
Keep some spare underpants and socks at work.