You can't buy creosote any more - banned as toxic and carcinogenic as are nearly all effective weed-killers other than glyphosate. Glyphosate is not particularly effective on ivy as it is absorbed through the leaves and ivy leaves are covered in a protective waxy coating
First thing to do is to cut through the main stem
Once you have cut through the stem of the plant you should be able to dig out the root without too much difficulty. Any remaining part of the root may start growing again so be sure to remove any new growth before it gets hold
The biggest problem is removing the stems from the brickwork. Cut back as much of the ivy a you can and then leave the stems to dry out - the longer the better. There is no easy way to remove the stems, which have extensive aerial roots, just hours of work with a scraper or similar prising the stems from the wall. I removed an ivy from my house 5 years ago and you can still see remnants.
Best to wear eye protection when dealing with ivy as the sap is poisonous. Do not put it through a shredder - I state this from practical experience as I ended up in casualty after the sap badly affected my eyes
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Ivy weedkiller 
Ivy weedkiller 