How to establish connectivity between a VPC in the Mumbai region and a transit gateway in the London region within the same AWS account?

Hello.

How can I establish connectivity between a VPC in the Mumbai region and a transit gateway in the London region within the same AWS account?

I think the following video will be helpful for setting up multi-region.
In case of multi-region, you need to create a Transit Gateway in each region.
You need to create a peering attachment to connect the created Transit gateways.
https://www.youtube.com/watch?v=cj1rQqLxXU8
https://docs.aws.amazon.com/vpc/latest/tgw/tgw-peering.html
https://docs.aws.amazon.com/prescriptive-guidance/latest/patterns/automate-the-setup-of-inter-region-peering-with-aws-transit-gateway.html

if I have an EC2 instance in the Mumbai region, would it be possible to connect to that instance from the London region after establishing this connection?

Communication is possible if the routing settings using Transit Gateway are configured correctly.

In order to establish connection across different regions, you will need to launch another TGW in Mumbai region and establish a TGW peering connection between both TGWs in London and Mumbai. You can then connect to EC2 instances in Mumbai VPC from London VPCs provided that no IP address overlapping.