When should probate begin?
There's no definitive rule on how soon after death probate should be started, but it's a good idea to begin this process as soon as you feel able to do so. You may find that you are unable to deal with any of the deceased's assets until you have obtained the Grant of Probate from the Probate Registry, and this can often take around 3 months to process, sometimes longer.
Some things that will need to be done straight after the death include registering the death, securing the property (if it's empty), contacting insurers to check that policies are still valid and notifying organisations such as the deceased's bank and government departments such as the Department for Work and Pensions (DWP) and HM Revenue & Customs.
https://www.probatesonline.co.uk/faqs/