Newbury is only served by GWR.
The note from the strike pages of National Rail about GWR reads
"Saturday 8 October - Strike day
An extremely limited service will operate. Services will start at 07:30 and all journeys must be completed before 18:30.
A very limited service will run on the following routes only:
- London Paddington to Bristol Temple Meads
- London Paddington to Cardiff Central
- London Paddington to Didcot Parkway
- Reading to Didcot Parkway
- Windsor, Marlow, and Henley-on-Thames branch lines
- Reading to Basingstoke
- Cardiff Central to Bath
Avoid travelling and seek alternative ways to make your journey. If you are intending to travel on these routes, please only do so if absolutely necessary. Trains that are operating will be extremely busy."
The line to Newbury is not one of those so OP making the right decision to look for alternatives.
Could you rent a car from Heathrow?