It depends on you. If you take the DIY approach to opening a company it might take longer. But if you use an incorporation service, it can take as little as 3 to 6 working hours.
Once your business is active (i.e. trading), you then have 3 months to register with HMRC (the UK's tax authority).
If you choose to start trading straight away, your company is 'active' and you must register with HMRC for corporation tax within 3 months.
Please note Companies House’s opening hours when processing your applications — they operate between 9am-5pm, Monday-Friday.