Are you sure? Because London isn't that far. :| I 'm not sure how I would change my plan to accommodate for that, because either way I am going to be charged extra.
I would say you should get a My-10 feature on your plan. I can't survive without it.
They're not far, but it's still long distance. I'm from Hamilton, and it's long distance to both Toronto and London. Brantford too, etc. Sometimes it's even long distance if it's the same area code (so stupid).
The best thing would be to ask rogers about how they charge you on long distance. They'd be able to tell you better than anyone else.
You can also get a $5 add-on which gives you 1000 LD minutes (canada-wide only) per month. These minutes still use up your regular minutes, so if you used up 200 minutes of LD, it would still deduct 200 minutes off your regular phone time, as well as 200 off your allocated 1000 LD minutes.
I work managing a call center for the/one of the largest cellular providers in the country doing technical support/customer service work. I have no knowledge of canadian providers, but I can definitely answer this question regarding American service.
Of our customers, 99% are no longer on the old school, grandfathered plans... The majority of our customers are now on plans that cover the entire nation so roaming charges are nonexistent within the states. (I know this isn't what you asked...) Along with these nationwide plans, the cellular minutes are used on a per minute basis to any landline or cellular line within the country. The only time you pay "long-distance" minutes is when you are making or receiving calls from an international phone number.
I obviously have no knowledge about the plan your parents are on.... but a quick call to your cellular provider (or probably even browsing their website/chatting with online support will likely answer your question with 100% accuracy.
tl;dr I'd say 99.999% you won't be charged long distance calls on a cell plan. (If you were American... I know nothing of canadian mobile industry...) Call your service provider. 
Canada = land of horrible phone plans. There is never enough competition in Canadian markets for companies to offer good, cheap services sadly. In America, most companies offer nationwide talk/text, but in Canada you pretty much have to pay a premium for it.
There are exceptions like smaller phone plan providers like Wind and Koodo. Koodo = no long distance within Canada. Wind has "wind zones" in which there's no long distance. Those are basically just all the big cities and major urban areas. If you're in one of those zones, you can call/receive to/from anywhere in Canada. Useful if you live in a bigger city, although coverage isn't as great for both of these options (at least I have heard). And also you mentioned you're still in a contract so there isn't really that option of switching companies.
Edited by Dangobear, 19 February 2012 - 10:33 PM.