Bicycle Tutor

I've just brought back my bike from the shop, was to sort out a wheel problem but have been told I need a new bottom bracket, until I reached this website I didn't have a clue what he was on about :-P
After seeing the videos on here I was wondering if this was fixable or if it would require a replacement.
When I push the pedal toward the frame on the drive side it moves about a 5 to 10mm at a guess. I tried to put it on youtube but you can't really see it moving.
If someone could point me in the right direction as the shop wants £40 for the part and labour and I'd rather fix it myself and keep the change

Do you know what type of bottom bracket you have? It's likely either a cartridge or a cup and cone...

It is a cup and cone bottom bracket, would it be a case of following the video to sort out this problem?

First you'll have to remove the cranks. Then take it apart and re-grease it for sure, as I'm guessing there's not much grease left in there. Check all the bottom bracket parts closely for wear and replace them as needed. Then when you re-assemble it make sure to adjust it so it's not loose but spins freely.

Thanks for the advise on boths questions, I will give it a try tomorrow and come back with my results/questions
Thanks again.