Close; you're right that 'put' is better than 'throw,' and that 'worth' isn't necessary.

But you need to take out 'it.' And you always need 'in,' but it can go before or after the object:

put one's two cents in
put in one's two cents
put one's oar in
put in one's oar
etc.

Instead of 'Let me' you can also say 'I'd like to,' which is a little bit less insistent. (-:

and what would be the most common British version of this?
"to throw in one's two pennies worth" as LEO suggests or rather "to put in one's two pennies" or something completely different?

my tuppence worth

I would like to add my two cents as well.

@PippiLotta: Leo also has "to put in one's twopenn'orth":
Dictionary: senf dazu geben
which is far more common IMO than the Leo suggestion that you found. The only phrase given in the Oxford Dictionary of English, 2nd edition (revised), 2005, is:
add (or put in) one's twopenn'orth informal contribute one's opinion.