The costs that you can claim depend on your personal situation. Some of the common expenses are listed below:
1. Laptops, tablets, other electronics as long as they are related to your work (not necessary a new one)
2. Mobile Phone bills
3. Stationery (paper, pen, printer, ink, envelopes, stamps, etc)
4. Home office running cost if you are working from home, check the specific reduction here.
5. Travel costs occurred when visiting clients (e.g. bus tickets, train tickets, flight tickets, hotel stay, fuel costs)
Try to make payement by credit or debit card for future reference, and always keep the receipts.
For more, you can read HM Revenue& Customs' help page.