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At time of writing there are no restrictions of any form when traveling between England or Wales. You do not need a test or to fill out a passenger locator form. However, covid rules in England and Wales are different once you arrive, and activities permitted in one may not be permitted in the other.
You mention you are traveling by train, be aware that many rail companies are still operating a reduced service.
Source: my own recent experience
I'll leave the arriving into England section for anyone that knows the current rules better. However, you do have to consider that you're day 2 test might be positive, you will be required to declare where you will be self isolating on the passenger locator form. Any positive results are automatically reported to the NHS. I'd highly encourage you to have a plan in advance for what you are going to do if this happens.