Difficulty removing pedals on Boardman bike

I once had to cut off the plastic pedal housing to expose the axle, remove the cranks and clamp the mostly rounded spanner flats into a solidly bench mounted vice then whack the shit out of it to release the fused screw threads

I had the same problem recently with a BTwin bike. Using a Park Tool Pedal spanner, I still managed to round-off the pedal flats! Was thinking about drilling out the pedal, but found an easier solution: 1-2 litres of boiling water, which seemed to give enough expansion to free the thread. And to overcome the rounding, I had to use two pedal spanners side-by-side, which gave enough grip.

try this:https://www.youtube.com/watch?v=qTtxoheAG10

I don't want to sound pompous but I think that the best thing to do is to invest in a good pedal spanner. In the meantime try putting some tubing over the hex key to get some more leverage. Stay safe.

It sounds as if you just need more leverage. Get a hex key with a longer handle. Or can you not use a peddle scanner? If they are factory fitted you should be able to use a peddle scanner on the 'outside' of the peddle. To loose the peddle stand over the peddle and turn towards the back wheel. 

Shops such as Halfords don't want the bad publicity of a customer's pedals falling off and might err on the side of caution by overtightening if the bike was built for you. 

If your existing pedals were supplied out of the box at the point of sale I'd be surprised if they only took a 6mm Allen key and didn't have 15mm flats on the spindles.  Do they? 

WD40.  Both sides.  You could extend the allen key leverage with a metal tube, as mentioned below, or threading the end through a ring spanner... Sometimes a knock with a mallet might help - if you can administer it accurately.  Wear gloves or cover up the chain ring (to avoid a nasty cut).  On my Ti / steel bikes I'd be happy to stay the frame by standing on the top tube (nearest the head tube or down tube).  If it's carbon I wouldn't bother...

Failing that...the bike shop where you got it. 

some sprays of Plusgas or similar might help.

are there flats on the outsides of where the pedals screw in that you could get a pedal tool around? 
 

If all else fails a gentle application of heat from a blowtorch to the crank arms at the pedals. This will allow the alloy to expand enough to extract the pedals. I'm not talking cherry red here, just 10 or 15 seconds worth should do it.

I would turn the bike upside down. Chock one crank against the chainstay with a stout stick (I use a wooden mallet handle). Put your Allen key in the other pedal, pointing forwards. Now you can push down on the tool with all your weight - even stand on it. 

You can extend the Allen key with a piece of pipe - I have an old flat MTB handlebar for this.

Repeat for other side. The orientation ensures you are turning the correct way to undo.

When refitting, use copper grease to stop them seizing.

Did you grease the threads when you put them on ?

Not wanting to insult your engineering skills but remember you are probably looking at the pedal from the back if you are using an allen key, are you sure that you are turning the right way, it is easy to get mixed up because of the rear view perspective.

Get some penetrating / 3-in-1 oil on there, liberally, and leave it for a bit (a few hours at least) and try again, adding more oil if they're still being stubborn. And if you can get a longer handle on the allen key that'll get you some leverage.