You can claim tax relief of £6 per week if you are working from home. if you pay the 20% basic rate of tax and claim tax relief on £6 a week you would get £1.20 per week in tax relief (20% of £6). That's a gain of £62 for the full year. A 40% tax payer would get £2.40 per week, a gain of £124 for the full year.
HMRC have made the process as simple as possible and you can claim the tax relief at gov.uk by following this link: https://www.gov.uk/tax-relief-for-employees/working-at-home
You only need to claim once for the whole year.
If you believe you have higher increased costs than £6 a week, you can claim more, but you will need evidence of the cost increases and be able to apportion these specifically to the fact you are working from home – and this becomes a much more laborious process.