job where I have had to travel like this on day 2
I have some idea of what you are facing. It's over two decades ago now, but my first day in the new job (based in London) I discovered the majority of my team were all based in Scotland. I was expected to visit them the next day.
Tickets, taxis and hotel for the following day were all arranged for me. I went home early that first day and wax in Edinburgh the next day.
All expenses were covered centrally.
In your shoes, I would expect that a hotel would be covered and be asking to make sure that I complied with their travel policy.
Ask whoever told you about the meeting in London tomorrow, how you contact the person who will make those arrangements, who will able to tell you which hotels are covered etc.
Good employers will want to ensure your your travel arrangements are smooth snd easy, to waste less of your working time and to acknowledge how often we travel on what is essentially our own time.
Travel arranged outside the 'hub' are frowned on because they do not qualify for the bulk discounts which will have been negotiated.
I typed all this and checked back in the thread. Glad to read you have find the person who will make the arrangements.
All the best in the new role.