How long does it take to get VAT and tax number for the UK company?

Unique Taxpayer Reference (UTR). You’ll get an activation code in the post within 10 working days of enrolling (21 days if you’re abroad). When you have your code, sign in to your online account to file your return online. (Link)  (Read: What is UTR number?)

Value Added Tax (VAT) usually takes at least 3 weeks to obtain.

Read more: 

• Starting a new business in UK
• Offshore bank account in UK