Which legal entity?
There are various ways to trade in the UK but the most common types for international companies are as a:
UK Limited Company
A limited liability company structure owned by shareholders and run by the directors. Quick and inexpensive to set up, with a corporate tax rate of 19%.
Limited Liability Partnership
A partnership but the liability of the members is limited. Easy to set up and transparent for tax - members all have to file UK tax returns and pay UK tax on profits derived from UK activities.
UK Establishment (Branch)
A UK establishment is the place of business or branch of an overseas company within the UK. Effectively a direct extension of the overseas company, officially registered at Companies House and the tax authorities to trade. Financial reports of the parent company are likely to be filed in the UK annually.