Heathrow to central london

I’ve posted before about a visit from a friend with limited mobility. It now seems that it will be easier for her to fly into Heathrow. From there she will need to get to Victoria main line.

I’ve tried asking the TfL journey planner for a step free route but it just throws a wobbly and spews out all sorts of weird routes. Plus it clearly wants people to use the express to Paddington. I would have assumed it would be Piccadilly to Earl’s Court for the District, or to Green Park for the Victoria line, then up to the main line concourse.

I could drive to Heathrow but I don’t have a blue badge, plus it’s likely longer by car than by tube and train.

Anyone on here have experience making that journey and know how difficult it is? Victoria has been in the process of being rebuilt for so long that I’m sure they must have put step free access in. The tube map says it’s step free!

Edited to add that another possible route would be via St Pancras and Thameslink to a nearby station with parking.