Apple is legally bound to honor warranties and support agreements in the country of sale, but as a practical matter, there are generally zero issues when you seek service from any country that has Apple Retail physical presence.
The worst case is you have to pay to ship the gear to the country of sale if requested and I’m not hearing that Apple requests it as a rule. The only exception seems to be iPhone that are sold in countries where carrier involvement is high…
For India you are in the “exception” category since Apple is not the primary person supporting AppleCare but a third party and that third party may not elect to cover you in UK if Apple doesn’t handle the repair.
Apple is saying the policy is global more clearly than it has in the past.
… only AppleCare+ gives you one-stop service and support from Apple experts, so most issues can be resolved in a single call.
- 24/7 priority access to Apple experts by chat or phone
- Global repair coverage1
- Onsite service for desktop computers:3 Request that a technician come to your work location or have a courier pick up your Mac for service
- Mail-in repair for portable computers:3 Mail in your Mac using a prepaid shipping box provided by Apple
- Carry-in repair:3 Take your Mac to an Apple Store or other Apple Authorized Service Provider
The 3 is most relevant for you - so be sure you visit the link in India to understand exactly what the contract there covers.
Availability of each option depends on country or region in which service is requested and location of Apple Authorized Service Provider. Apple may also request that the customer replace components with readily installable parts.