Any advice on how to reduce taxable income to lower taxes owed?

Wondering if anyone can advise on ways to lower ones taxable income. I looked at the HMRC site and it seems you can take some deductions for expenses paid as an employee or expenses paid as a self employer.

I'm curious if I decide to operate my side business while employed in the UK can I deduct my company expenses to reduce my overall total income (from my employer and any income I receive from my side business). Can the deductions be applied to both (or total) income?

In Japan I operated a side business and was able to deduct my business expenses related to my side business to reduce my overall income which in effect lowered my total income and put me in a lower tax bracket so I was able to get a rebate of tax money I had paid in.

I was walking around Ealing Common the other day and noticed a bunch of tax accountant offices advertising that they can lower your taxes. Just curious what they would do to do this. Thanks!