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There is no reason why you cannot be self-employed and retired at the same time. If you are self-employed but work in a fixed place, you cannot claim tax relief for the home to office and office to home trips. If you work at different places and have multiple clients, then I would be inclined to claim the travel expenses.
I hope this helps but let me know if you have any further questions.
You can claim them. You say that you go to different places which makes the costs deductible even if you have one main client. If you were going to the same place every day, eg the client's head office, you would not be able to claim those costs unless you worked from home and rarely went to the head office.
I'm just following up to find out if my answer helped or if you have any further questions.