Upvote:2
I'm not familiar with the UK system, but I can describe the Canadian system which I believe is broadly similar.
On arrival a border officer is going to make an initial assessment of your claim. Obviously frivolous claims will be rejected. If you dump your passport on the flight this will be an immediate cause for suspicion, as they know you needed your passport to get on the flight. The airline will have a record of your passport number. If it looks like you are trying to fraudulently enter the country you may be arrested and probably deported.
Assuming your claim is not obviously invalid, you are allowed to enter the country and given a certain amount of time to explain why you need refugee protection. Then a certain amount more time to back this up and provide evidence. A decision is made by a refugee official at a formal hearing.
The likelihood of success is entirely dependent on the case you make for being in danger in your country, and the quality of evidence you can provide to back this up.