Her Majesty’s Theatre (soon to be renamed His Majesty’s again) has decent accessibility, but it’s worth planning ahead. The entrance is step-free via Haymarket, and there’s a wheelchair-accessible space in the Stalls with companion seating right next to it. The Circle, Balcony, and Amphitheatre aren’t really accessible, since they involve a lot of stairs.
There’s an adapted toilet near the Stalls, and the theatre recommends booking wheelchair spaces directly through the box office rather than third-party sites. Staff are generally very helpful with access needs, but it’s not a modern building, so options are limited to ground-level seating.