There's no charge of 'breaking and entering' under current English law. (The legislation which used that term was repealed by the Theft Act 1968).
The current relevant charge, where appropriate, would be one of 'burglary'.
The Theft Act 1968 defines 'burglary' as trespassing with intent to steal (or actually doing so), with intent to commit grievous bodily harm to any person in the building (or actually doing so, or attempting to do so) or with unlawful attempt to damage the building or its contents.
So you're not committing burglary if you enter someone else's property other than as a trespasser (which you wouldn't be if they'd asked you to force entry). Even if you did enter as a trespasser, you still couldn't be charged with burglary unless you intended to steal (or to commit one of the other acts mentioned above). It's not an offence simply to go into someone's house, even if you've not been invited in. (If you see that someone has left their front door open, it's perfectly legal for you to walk in and look around, as long as you have no criminal intent).
The only other possible charge that you might face could be one of 'criminal damage' (in relation to the 'breaking' part of 'breaking and entering'). The Criminal Damage Act 1971 makes it an offence to damage someone else's property 'without lawful excuse'. It's a 'lawful excuse' to damage someone else's property if you genuinely believe that the owner of the property (or someone else who has control over it, such as the tenant of a rented house or the manager of a shop) has given permission for you to do so or (if, say, he's not present) that he would have given consent if he'd known about your intention to cause the damage.
All of the foregoing is really a long-winded way of saying that the "someone told me I could get into trouble for it" was talking utter b*ll*x!