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Hi.If your work place has been moved permanently, you will be taxable on any reimbursement of home to work travel costs by your employer from day one I'm afraid. Unfortunately, you cannot claim tax relief for the costs of travel from home to a normal place of work. See chapter 2 and, in particular, paragraph 2.5 of the Employee Travel booklet here. There is no period of grace unless your move to a new work place is temporary and not likely to last more than 24 months. See paragraphs 3.11 and 3.12 of the booklet here.
As well as having to pay tax on the reimbursed travel costs, you may have to pay national insurance contributions. Whether you do or not depends on how the costs are met by the employer. See chapter 6 of the Employee Travel booklet here.
There is no obligation on your employer to pay your travel costs. They are doing it to help you and presumably others to help with the extra travel cost. Many employees get no such help. The employer can pay the tax and NIC for you if it agrees a PAYE Settlement Agreement with HMRC but I'd be surprised if they entered into one of those. I hope this helps but let me know if you have any further questions.