My sister and mum(84) will come from Paris via chunnel and have one last night in London before our 10:30am flight. Looking for a low- cost accomodation with easy connections to the airport.
If low cost is a big factor then probably Kings Cross / St Pancras where you get off the Eurostar train is the best for you.
In the morning you can get the London Underground direct to Heathrow direct from St Pancras for a maximum fare of 4 GBP each.
The B&B hotels around Argylle Square opposite St Pancras probably offer the best value accommodation in London. You'll typically pay about 60-65 GBP for a double/twin with breakfast. Best places include Wardonia, Crestfield and Montana Excel. These places don't have lifts though so if your mun finds the stairs an issue probably the best place is the Premier Inn next door to Kings Cross Station an excellent budget chain hotel.
I am going to London for a week in December. My last night in London will be near Paddington Station. The Heathrow Express and Heathrow Connect pick up there and go directly to Heathrow. I, Too, will have a flight out of Heathrow and want to get there early!
I am using the EasyHotel Paddington, the rooms are only 29 Pounds a night right now. Its a basic bed and shower, nothing fancy, but definately affordable!
WE were at the Premier Travel Inn County Hall near Westminster Bridge. You can arrange (direct phone in lobby to a taxi company ---not a traditional black taxi) to pick you up. I made arrangements the day before and the driver was promptly there at 6:30 am. The cost was about 30 pounds with tip for 3 people. Well worth it!
This is a tall order for you Mum. Look into Travelodge Inn online.
How well does your mum walk? Some 84 year olds can climb Mt. Everest and others have trouble with stairs, walking a block, etc.
If she can walk, then either train or tube should be fine assuming you don't have a lot of luggage. If you stay near Paddington then the Heathrow Connect is convenient and fairly inexpensive. If you stay somewhere else, you might want to find a place near the Piccadilly line. This way you won't have to change trains to Heathrow.
Or, you could take the coach from Victoria Coach Station. Less walking than the tube and there are lots of places within a block or two or the coach station.
If she has trouble walking or with stairs, take a taxi.