Downpipe Blockage

danrv

Check the condition of the render as mentioned. My garage is the same construction although not rendered or painted inside. 
Water was coming in a rear corner due to gaps in the external mortar. Have repointed the area, sealed the inside and it's ok now.
Roots from a large Beech tree probably didn't help either but I've cut that down. 

newbieni

Unfortunately, the garage was as damp as ever today. I took the panel off side and it probably an issue that's bigger than a blocked downpipe.

stuart45

The ground level has probably got higher over the years with all the leaves collecting in the gap. The floor will also take quite a while to dry out. 

WIAWSNB

Sorry, got it wrong - it's single skin brick, and not block. And no external render.
However, the fact it's painted, with no obvious sign of 'penetration', still suggests the issue is coming up from the ground. 
A closer look at the internal pic shows damp coming up a fair deal in the corner.
So, suspect it's a 'rising' issue, likely down to the exceptionally wet recent weather.
As Stuart has pointed out, it's worth starting with a good clean-out of that gap. You may need to cobble up a suitable tool like a long and narrow hoe, and scrape away.
Check the ground in that external corner - is it puddling? 
And, how do the relative levels compare?

Eldi_Dos

To clear out that space I would try a small soil Flower rake, less than 100 mm wide securely attached to a decorators extension pole.

Swipe

As above, it looks like the ground is water saturated to me. 

WIAWSNB

Could we see that whole external corner, Newbieni?
Is there anything preventing that side, and front, from draining away?
Any surface water outside?