[st0ne5ish]

The land my new plot is on used to be grass, the farmer ploughed it over before marking out the allotment plots.

I've put out strawberry runners, onions, garlic and some fruit bushes.

However now the grass is starting to grow back up, I have already marked out and dug my beds over adding manure so it's not as bad as those peoples who have not yet done this, a lot of plots now resemble lawns.

I guess my options are to try and pull it out as it comes up, this is a pain as there are a lot of individual shoots or add some kind of mulch/barrier?

Would covering the whole of the unused beds with cardboard be a good idea? Would that kill of the grass completely if I leave it there till spring?

Adding cardboard between the onions/garlic/strawberries would be a lot more difficult.

[Yorkie]

I doubt it would kill off couch grass (the one with thin white roots like piano wire), might kill off regular grass (fibrous roots) but of course plants are going into dormacy now so you might find they regrow in spring.  Can't do any harm though, if you have the cardboard to spare.

[Weston grower]

You will probably never "get rid" of the grass but you can "control" it. You need to keep on top of it with regular digging/weeding. For some while it will seem a thankless task but after a year or so you will notice that you have a lot less of it than your neighbours who leave it until the spring to deal with.

Make sure you break the soil down when you dig and remove all weeds/roots.

Do all of the things you mention on your existing beds

How do I know this - I'm a year in front of you. 

Cheers, WG