Well we could go on forever on this one but briefly:

In UK usage, a melodeon is a diatonic button accordion. It can have one, two or sometimes more rows of buttons on the right hand, each row playing in a different key and a small number of buttons on the left hand which play a mixture of bass notes and chords for the keys on the right hand. All buttons play different notes on opening or closing the bellows. The most common keys for a two row melodeon in England are G and D which are the keys (and their related modes) most commonly met in English Folk music.

There are three types of concertina. The English, Duet and Anglo concertinas. The English and Duet concertinas are fully chromatic can be played in any key. Each button plays the same note on both on opening and closing the bellows.

The Anglo concertina was originally diatonic with two rows of buttons, each row playing in a different key. Each button plays a different note on opening and closing the bellows. The most common pair of keys for the Anglo Concertina is C and G but other key combinations are met: D and G (popular with Morris Dance musicians), Bb & F and occasionally other keys. Many (most?) Anglo concertinas now have a third row of buttons which provides the extra notes needed to be able to play in any key and thus renders the instrument fully chromatic at least in theory, but the anglo is still at its best in its two home keys and one or two closely related keys.

The OP has an anglo concertina. Whichever she takes with her she will have an instrument capable of playing almost anything you are likely to meet at an English Folk festival session. It's really a matter of taking the instrument you are most comfortable with.