Yes they can. HMRC can collect outstanding income tax via your tax code – meaning your employer must pay it to HMRC without you having a say. This can put a massive strain on people’s finances while HMRC gets paid before the mortgage etc. If you earn less than £30,000 p.a., HMRC will not collect more than £3,000 of unpaid tax per year – above this there is a graduated scale (up to a maximum of £17,000 per year). Also, the tax collected under PAYE cannot be more than 50% of gross wages or salary.
Having said this, I have never actually seen this happen in practice.