I'm referring to what I read on the Natural History Museum website:
Walk-up entry is not permitted during half-term 12-20 February. At 17.00 each day throughout half-term, a limited number of tickets will be released for visits the following day.
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Most dictionaries only list the (mainly US) meaning of simply 'walk-up' as 'related to apartments in buildings with no elevator' but the meaning in the question is often used in the UK in relation to the price of tickets for travel by train, admission to events, museums, etc, and usually means 'the standard price without any advance discount'. In the UK, many rail tickets are cheaper if they are bought in advance, and the price charged if an intending passenger comes to the booking window ('walks up to it') and wants to travel immediately is called the 'walk-up fare'. So here a 'walk-up ticket' to the Natural History Museum is one obtained by arriving when one wishes to enter.
Although entry to the Natural History Museum in London is free, the number of visitors present at any time is regulated by the use of tickets.
noun [ C ]
the price you pay for something such as a ticket if you buy it just before using it, rather than buying it some time earlier:
Example: tickets booked online for the same day will be charged at the full walk-up price.
"Walk-up entry" means what it seems to means. It means you walk up to the door without pre-arrangement, buy a ticket, and get in.
This seems to be because it is half-term. That is a short holiday in the middle of the school term. This phrase is very specific to the UK. There are similar holidays in some other countries. For example the US has spring break, which is mostly for university students.
So during half-term holidays, there may be lack of staff because the staff are home with their children. Or there may be too many students since they need something to do in the winter when school is not in session. So during this holiday, the museum must make these arrangements limiting access to the museum to a small number of tickets released the previous evening.