Can I go to his funeral?

I would think if you go it will depend on the local rules whether or not you can stay with them.You would need to self isolate when you come back .My relatives in England didn't come north for a family funeral in April because of lockdown .There are only very small numbers allowed at a funeral now and no wake after it ...dont know if its the same in England.You need to chech with someone in Manchester for the rules there .

I would imagine that the new lockdown in England means that you will not be allowed to travel so far.

I think it is quite clear that you cannot!

According to the guidance it’s not forbidden, but you are strongly advised to follow the national tier restrictions. You definitely can’t stay in another household, but you can attend the funeral, subject to any restriction on numbers which my be introduced after todays announcement.
www.gov.scot/publications/coronavirus-covid-19-guidance-for-funeral-services/

i've just clicked on the link you've given Casdon and it states that it was last updated 30 NOV 2020!

That’s right, it’s law until it’s changed, it’s also clear on taking heed of the guidance in force at the time. If funerals are permitted to have family members present, then this will apply.

● Communalw worship and life events
You can leave home to attend or visit a place of worship for communal worship, a funeral or event related to a death,​ ​a burial ground or a remembrance garden, or to attend a wedding ceremony.​ ​You ​should follow the guidance on the safe use of places of worship​ and ​must not mingle with anyone outside of your household or support bubble when attending a place of worship.Weddings, funerals a​nd religious, belief-based or commemorative events linked to someone’s death are all subject to limits on the numbers that can attend, and weddings and civil ceremonies may only take place in exceptional circumstances

From tonight’s guidelines - sounds like a qualified “Yes” but not the staying overnight. I cannot see why a hotel would not be permissible though.

The way I understand it you can go to the funeral but you'll have to go there and back in one day. There can be 30 people at the service but only 6 at the wake.