As the work you do for the out-of-hours organisation is on a self-employed basis, you will be able to claim for the business expenses related to that work including motoring, professional use of your home, computer and telephone costs.
You can claim a percentage of all the costs of running a car (or other vehicle) including fuel, insurance, road tax, servicing, repairs and cleaning. If you are buying your car on hire purchase or you have a loan, a percentage of the interest can also be claimed.
Capital allowances pro rata to business use for the wear and tear (depreciation) of the car will further reduce your tax bill.
You can claim for work done from home for the out-of-hours organisation. Your options for this are either a fixed amount a week or a percentage of the running costs of your home (GPs' accountants usually negotiate this with Revenue & Customs).
This may trigger a capital gains tax bill when you sell the home if you use a room exclusively for business purposes. The business use (self employment) elements of home telephone, mobile phone, home computer including internet costs are also allowable.
Other allowable expenses include the business element of medical subscriptions, medicines and instruments, medical books, journals, postage and stationery.
Incidentally there are likely to be some work-related expenses you can claim against your salaried income. Ask an accountant to advise you, the rules are less generous than the ones for self employment.