Only excuse.... Can you disturb the life in London this long? No, you'll be jailed second day...
And this time by civilians.... Score levels.... Times now to uproot it to get a lead, eh?
No actually such demonstrations are not allowed in the first place and it is simply not possible due to the fact that UK has established democratic system in place. Here the thought of army coup is not possible, they allow the government to complete the tenure even if they have performed really bad, the Prime Minister and the cabinet might be reshuffled but the elections are usually held on time.
Basically first of all you don't seek permission from the government to hold protest in UK. In UK, if more than 4-5 people (I can't remember the exact number now) are gathered, it is considered public gathering and it is not allowed without seeking permission from the police. If the police arrives at spot, they will simply start questioning everybody and may arrest you.
If you want to hold protest, you will first have to inform the police, explain the cause of protest, route you are planning to hold at, seek permission from each party involved (people, borough/local councils etc). So basically if you want to hold gathering for about 1 mile, it is very likely that you might be crossing 2 different boroughs, so permission from both boroughs is needed. Moreover I don't remember any protest taking place for more than a day. You simply give the written declaration to the police about the right, the time it starts and ends. There is no such thing as red zone so small gatherings around the parliament are always happening but that is only for couple of hours maximum.
The police has the right to refuse the protest and they can cancel the event at any time. Anything that goes beyond the plan can lead to immediate arrest and also the police is the final authority to organise a route. So I have heard that many times if your route is like 1 mile straight ahead, the police might refuse you to enter certain parts of the road and will make a big round of the route and the same journey might be completed in 8 miles