On their website, TfL says both things:
1. The map is covered by copyright.
2. The only way to get a license is to buy one from their map partner.
> We protect the map under copyright and officially license it for brands and businesses to reproduce it.
> To use the map in your design, you must have the permission of our map licensing partner, Pindar Creative. This is the only way to officially license the map, no matter how you'd like to use it.
Yet, they don't even mention the case you might be a third-party developer providing a non-profit service.
https://tfl.gov.uk/info-for/business-and-advertisers/map-lic...
> For registered charities and schools, the licence is royalty free, but we still charge an artwork fee of £352 + VAT
https://tfl.gov.uk/info-for/business-and-advertisers/using-t...