Look at it the other way:

Would your employer give you more than the minimum legal notice if they were thinking of firing you or making you redundant?

The answer to that is probably "no".

The notice period in your contract is there to notify your employer of your intentions to leave. In some countries/industries you get escorted from the premises as soon as you hand in your notice - for all sorts of reasons. These same reasons would apply when you reveal your intentions to move.

In respect of a reference - in the UK all that a previous employer has to give is confirmation of the dates you worked there. So there should be no issue of not asking for a reference.

It is not expected that you inform your boss that you are looking for a new job, and it's certainly not required.

Look at it the other way:

Would your employer give you more than the minimum legal notice if they were thinking of firing you or making you redundant?

The answer to that is probably "no".

The notice period in your contract is there to notify your employer of your intentions to leave. In some countries/industries you get escorted from the premises as soon as you hand in your notice - for all sorts of reasons. These same reasons would apply when you reveal your intentions to move and if the move didn't happen then you'd be in an infinitely worse position than you were before.

In respect of a reference - in the UK all that a previous employer has to give is confirmation of the dates you worked there. So there should be no issue of not asking for a reference.