The £4,250 tax free amount is available if you are using the 'Rent A Room' scheme. Under 'Rent A Room' a taxpayer can be exempt from income tax on profits received from renting part of their only or main home if the gross receipts (that is, before expenses) are £4,250 or less.
If the receipts exceed the £4,250 exemption limit, you can choose to be taxed on the gross receipts above the exemption as an alternative to preparing the standard profit and loss account. This may in some case be more favourable if the rents only slightly exceed the exemption limit to save on administration costs of preparing the accounts.
Unfortunately, as you own the property with your wife, you cannot both benefit from the exemption limit of £4,250. If more than one person is letting a room in the same home, the limit is reduced to £2,125 for each person receiving rental income.
The 'Rent A Room' scheme only applies to ordinary lettings of living accommodation in the taxpayer's own home. You cannot apply it where the rooms(s) are let as an office or for other business purposes.
You should ensure that when claiming 'Rent A Room' you calcuate that this is more beneficial than establishing your profit after expenses, as you have the a choice of which method to use.