I'd start with raking out the crack on the outside. If large then fill a mix of 4 parts sand to one part cement. Add some pva to the to help it stick and be more workable. If the gap is small then use a good quality exterior mastic, not silicon. You could apply a coat of clear water proofing liquid to the brickwork.
Wait and hopefully the inside will dry out. This way you will know for sure if you have solved the problem.
If so then fill with any water resistant medium you have, sand and cement or expanding foam. Only then should you think about making good with new skirting.
A word of warning, based on my experience of last winter. Our new build mdf skirting boards were fitted tight against the plastic door frames. In the very cold weather we had condensation on them that was absorbed into the ends of the skirting and made them swell. I removed them, made new and aluminium primed all surfaces before fitting with a 2mm gap up to the door frames. After painting I masked the areas and applied a white silicon to te gap.
Colin