Wheelbarrow tyre leak at base of valve

The tyre on my old builder's wheelbarrow has a leak. It's been like this for some years and remained unused, hence the axle is also rusty (but I've freed this up now).

By inflating it and placing it in water I can see where the leak is coming from, namely where the valve enters/exits from the red plastic wheel.

The wheel and tyre looks like this one:

http://www.amazon.co.uk/Pneumatic-Wheel-Replacement-3-50-8-COMPLETE/dp/B002U6676S#Ask

I'm tempted to buy that, but another problem I have is that the axle that goes through the centre of the wheel appears to be rusted/fixed in place, so I would also need a new wheel axle as trying to bash out the axle would no doubt break the plastic wheel. The axle itself rotates okay where it is fixed to the barrow's fork.

So, how could I fix such a leak? Any ideas please?

Thanks

EDIT: I'm an idiot - for some reason I thought it was tubeless but now I see that it can't be. I'll remove the inner tube later and see if I can patch it up.

There's a good chance the inner tube is well goosed......the leak could be anywhere on the tube and the air just shows at the valve hole.
Its usually possible to fish the tube out if you can break the seal between the plastic rim and the rubber tyre, but a better fix is to fix a solid rubber wheel in place if you can.
These are available from the usual sheds.
John

Thanks, for some reason I just assumed that it was tubeless. But now I see it's not. Ta for the suggestion.

I might though try and extract the inner tube - if there's an obvious leak I can patch it up with my bike's puncture repair kit.

Yup, inner tube leak - now to find my bike's puncture repair kit ..........

If I get another puncture I'll invest in a solid rubber wheel/tyre.

Feel inside the tyre carcass for that elusive thorn!
John

Will do!

But wear gloves or you will need to buy some plasters as well!

Steel gloves?

All sorted now - patched up very nicely, holding air fine, no more leaks, and no thorn found either (must have been an "in and out" job )