Any withholding tax deducted is a payment on account of the final UK Income Tax liability. The liability can be revisited after the end of the tax year by either the taxpayer or HM Revenue & Customs (HMRC). Where it seems likely that some material year end adjustment, including a repayment, will be required, a return will be issued. However, if tax has been paid as nearly as may be to the final liability in year via an artiste reduced tax payment application (see Reduced Tax Payment Applications) HMRC will not normally require final filing of a return.
Many non-UK resident individuals (including all EU citizens) are now entitled to UK personal allowances. There are, however, still some notable exceptions - particularly the USA. A very good guide to those entitled is reproduced in the Notes to the Non-Residence pages of the Self Assessment Return (page NRN7). See Tax Returns and Notes in the main Self Assessment section.
To minimise the amount of end of year adjustment work, Foreign Entertainers Unit will give personal allowances in year (eg in calculating the tax to be withheld as part of a Reduced Tax Payment Application) where the information available suggests that allowance is likely to be due. HMRC will give personal allowances in such circumstances regardless of whether or not an actual claim has been made. Inevitably, there will be some cases where allowance might be due but where the entitlement is not clear from the information available. In such cases it will be for the individual to make a claim.
If final filing is required, whether by you or HMRC, a useful starting point is the Helpsheet specially designed for non-resident entertainers and sportspersons, the HS303 (PDF 171K). If additional information, including a Return and schedules, is required this can be obtained from the Foreign Entertainers Unit. Further information on Self Assessment generally can be found on the Self Assessment pages.