London Heathrow Airport: Lechlade has no rail station, so a hired car is the genuinely good option: roughly 1 hr 30–2 hr via the M4/A419 or A40/A361, depending on traffic. Public transport is possible but poor value with luggage: RailAir coach to Reading, GWR to Swindon, then a pre-booked taxi for the final 30–35 minutes; allow about 2 hr 45–3 hr 30 and roughly £55–£90 total.
Bristol Airport: Hire a car; allow about 1 hr 45–2 hr 15. There is no clean airport-to-Lechlade public-transport transfer, and stitching together airport bus, rail and a taxi is a long day rather than a saving.
Swindon railway station: The best railhead from London or the west. Take GWR from London Paddington (about 55–70 minutes), then pre-book a taxi to Lechlade: around 30–35 minutes and commonly about £40–£55. Do not assume there will be a taxi rank supply adequate for a late arrival.
Oxford railway station: Useful if arriving from Birmingham, the Midlands or Oxford itself. A taxi to Lechlade takes roughly 45–60 minutes and is usually around £60–£80. Buses are not a sensible airport-style transfer: connections are limited and can turn a one-hour road journey into several hours.
Kemble railway station: A workable Cotswolds railhead, especially from Paddington via the Cotswold Line, but not a magical shortcut: it is still about 35–45 minutes by taxi to Lechlade, commonly £45–£65. Arrange the car in advance.