The Beloved Prophet صلى الله تعالى عليه وآله وسلم said,
“Whoever intends doing Qurbani should avoid clipping his nails or cutting his hair for the first ten days of Dhul Hijjah.” [Sunan an-Nisa’i 4362]
This is mustahabb (recommended) and not wajib for the one who will be giving Qurbani; so if someone does clip his or her nails or cuts their hair there will not be any wrongdoing and the Qurbani will still be valid. After the Qurbani has been given one may clip nails and cut hair.
In the UK, there is a possibility that the 1st of Dhul Hijjah will fall on Wednesday 23rd of August so those intending to give Qurbani ought to clip their nails and cut their hair before sunset on Tuesday 22nd of August.
Allah knows best.
Answered by Mawlana Shahid Ali