I really don't know how many employers that would refund a £500 taxi because the trains were off.
Some would, particularly for the likes of "C-suite" (i.e. CEO, CFO, COO etc) people (who also, if on telephone number salaries, may consider it simply not worth the effort of claiming!)
Regardless I cannot see it being valid for tax purposes as it would be normal commuting.
It won't be for all of them, but even so this doesn't bar a company from paying an expense, they can if they want, they just have to "gross it up" i.e. pay more so as to cover the tax and NI on it as well, and pay it through the payroll rather than separate bank transfer. My employer has a process for doing that in the employee handbook. Rarely are our contracts long enough not to be temporary workplaces, but it can happen if e.g. one member of staff gets several central London contracts in a row, and in that case if they can't avoid it by swapping people around to different contracts the expenses are still paid but grossed up so the tax is correctly paid on them.
Companies very often say "that's not claimable as it'd be taxable" which is just an excuse for "it is outside our policy to pay that". They can pay literally anything they like, they just have to pay tax on it too if it's outside the HMRC rules for tax-free expenses.
I can see pre Uber people sharing in the taxi queue, but now everyone uses apps they will be all over the place and hard to group together.
They'll be grouped together on the Waterloo concourse and will recognise people from their daily train even if they never talk to them normally!
And the fares will be absoluely eye watering if everyone is trying to pick up from Waterloo at the same with surge pricing.
I'm not sure why that's their problem.