Can I claim expenses I paid before I started trading?

Yes, HMRC allows you to claim pre-trading expenses that were incurred wholly and exclusively for the business in the period before you started trading, typically up to seven years beforehand, as long as they'd have been allowable if the business had already started. These are treated as if they were incurred on your first day of trading, so they reduce your profit for that first tax year. Keep receipts and a note of what each cost relates to, since HMRC may ask you to justify the business purpose given the gap in timing.