So I'm guessing you mean 7k in Canadian Dollars right? Which is equal to £4244 British Pounds.
I think you'll definitely have enough money to get settled in and find a job, so long as you manage your budget and are committed to finding work.
I can understand your parents' concern, I'd be a bit worried if my daughter moved to London on her own at 18, but as long as you use your common sense you should be fine.
Will you be travelling alone or with friends? It might reassure them to know that you're keeping good company and won't be led astray by the London folk ;)
Anyway, here's some general advice you might find helpful:
Finding a place to stay in London.
One hurdle you'll need to jump is accommodation. A single room in a shared flat will probably cost anywhere from £400-500 pcm upwards depending on distance from center of town, transport links and what the area is like.
Generally, the less you spend - the worse the place will be.
There are occasional bargains out there, but overall London is an expensive place to live and personal space is a bit of a luxury.
Gumtree.com is the most popular site for finding rental properties and flatshares. If you're planning to share and not travelling with friends, I'd seriously suggest taking your time to find the right match.
Not only will this be your new place to stay, but having the right flatmates is going to make a whole lot of difference to how much you enjoy living in London.
Finding work in London
Like any capital city, there are more jobs going in London than the rest of the UK. What you end up doing will depend on your qualifications & ability, what you'd like to do, and a bit of luck always helps too.
I'd suggest getting in touch with recruitment agencies before you fly and setting up an interview with them. Also have a look at the job market (Gumtree.com also does job listings, but depending on what sector you want to work in, there may be better suited listings pages).
If you're just looking for casual work in a bar or restaurant, that should be pretty easy to come by.
Your work visa might restrict you to the number of hours you can do, I'm not sure - but it's something to take into account when you plan your budget...
If there are any specific questions you've got (like what areas to avoid, where to go out, how to claim money back from the taxman when your stay in the UK is up) please feel free to ask and I'll do my best to answer!