I think your question was about finding out the kinds of expense you can claim - that would be all expenses which you have to incur in running the business... including costs of travel, office, working at home, communications, marketing.. all the normal ones. If one sees turnover of £100k and self employed expenses totalling £35k that would be normal.
The difference between self employment and employment in the UK when it comes to deductible expenses is a more stringent test for the deductibility of expenses from employment income (which broadly is that every holder of that employment must also be obliged to pay for that expense) - so what you know from Japan is true in the UK, but less so. The second difference is in National Insurance contributions for State benefits - less for the self employed but also less State pension benefit. The third difference is in the employment rights persons in employment have are far greater than those of a self employed status (see maternity pay, holidays, termination).
Tax trap: IR35 will determine some self employments that have the badges of 'employment' as the latter and will require the firm paying your wife to put her on the 'employed' payroll. To avoid this trap take advice or read widely.
If I was planning this, I'd consider leaving the business in Japan as a company, and using that company to employ you as employees in the UK.
There's no single guide to filing in the UK. You are pretty much thrown in the deep end.
