Sounds like you may have water in the fuel?
It's not so bad when it's all stirred up, especially with some ethanol content (which absorbs water), but after it sits for a week the water (being heavier than petrol) settles to the bottom of the tank where the fuel pickup is.
Normally I'd say it'd have to be the petrol station that has water in their tanks, but as you've only had the car a couple of weeks you don't have a good baseline to say for sure?
The proper way to fix this is to drain and remove the fuel tank to clean and inspect it, possibly use one of those "treatments" that coat the inside if it's rusty, then flush the fuel lines and change the filter(s).
Or the bush mechanic's method would be to run the tank down until it's under a quarter then add a litre of metho. But don't let the metho sit in the tank for any length of time, once it's in, go for a drive to slosh it around and run the tank as dry as you dare, if you've got a good battery and a jerrycan of petrol with you, you could even run it out altogether, then fill it up again WITH GOOD CLEAN FUEL.
BP Ultimate is my first fuel of choice, these days I'll drive out of my way to find it. If you look at the composition of all the different brands of fuels in their MSDS you'll see it has almost no additives (see BP Ultimate sheet here) but it comes down to your local area and what kind of choice you have too. Caltex Vortex 98 would be my second choice (MSDS here).
Shell V-Power on the other hand...
Contains Benzene, CAS # 71-43-2.
Contains Toluene, CAS # 108-88-3.
Contains Ethylbenzene, CAS # 100-41-4.
Contains n-Hexane, CAS # 110-54-3.
Contains Xylene (Mixed Isomers), CAS # 1330-20-7.
Contains Naphthalene, CAS # 91-20-3.
Contains Cyclohexane, CAS# 110-82-7.
Contains Tri-methyl-benzene (all isomers), CAS# 25551-13-7.
May be dyed. Red.Purple.
...I would have to be REALLY desperate to use!