I did a teddy bears picnic (as documented in length on this thread and the last one
) last month - ask me anything! It was for my daughters 2nd birthday but we had 25 children aged from 5 months to 13 so I think most of the activities would be OK for you.
We had a 'picnic' on little tables but you could easily move it onto the floor. I bought 10 red gingham disposable tablecloths on ebay for less than a tenner which looked really picnic-y and could be thrown away afterwards to save on cleaning up as we had hired a hall so needed to be out fast afterwards. You could buy a proper cotton one if you wanted to save on waste. We also had lots and lots of bunting which really made it feel village fete/picnic-y too. I'd bought tonnes of balloons but most of them popped before the children even got there 
Sandwiches went down well as did chicken nuggets, mini sausages and fruit - and of course Pom Bears :)
For activities, the favourite by far was the Gingerbread bear decorating. Even some of the adults joined in. I made enough bears so that everyone had 2 each and made little bowls of powdered icing up then put out pots of decorations. I raided my baking cupboard and then went a little mad in the Supermarket home baking aisle so there was plenty of choice and the children loved dressing thier little bears. The other popular one was colouring. I printed out lots of free colouring sheets from the internet then put out some crayons and a big tub of foam stickers I got from Hobbycraft. Some of the children made pictures to take home and quite a few made extra cards for DD, it was lovely.
The activity we nearly did was to make teddy crowns, both for the teddies and with ears stuck on for the children but we ran out of time in the end. I looked everywhere for a teddy-bear-pin-the-whatever-on but couldn't find one to buy and ran out of time to make one.
I did manage a pass the parcel with a teddy in the middle though. I got a cheap one from Ebay for a few pounds and birthday wrap from poundland. I put packets of Haribo in the layers. I'd wanted just jelly teddies but couldn't find any so they ended up with starmix instead as it has teddies in.