Heather,
Are you on a contract plan with Rogers or PAYG? I'm not sure PAYG customers have the ability to roam, but if you're on a contract it's very easy.
If you're going to buy a new Phone, BE SURE that it's a quad-band GSM model. When I was in Italy recently, I spoke with a couple of young travellers from the U.S. that were very puzzled on why their phone wouldn't work in Europe. After all it was a GSM phone. I checked the settings for them and it turned out the phone was only equipped with the two North American frequency bands.
You could certainly buy a Phone in the U.K. as there are shops from the various networks on almost every street corner. Carphone Warehouse has lots of branches as I recall. However, two things to keep in mind. When you use this in Paris and Amsterdam, you'll be paying higher rates than in the U.K. The E.U. has been pressuring the cell networks to reduce roaming charges, and they've had some success but I don't think the rates are as low as they would like.
Also, if any of your family and friends will be calling you, they'll be required to dial (and pay for) long distance to the U.K. Be sure they know the correct number sequence. If you roam with Rogers, callers simply dial your regular number and the network will find you (keep in mind that incoming calls are more expensive than outgoing local calls, as these are routed from Canada).
If you use Rogers, be sure to phone customer service and tell them you'll be travelling with your phone. If you buy a phone with data capability (I-Phone, Blackberry, etc.) BE SURE to disable the data section as data roaming is VERY expensive.
Whichever option you choose, you'll have to spend a some time in a cell phone shop (either at home or in the U.K.) to get it sorted.
Hope this provides the information you need?
Happy travels!