Hello @adam18 - nice to hear from you again!
Since you applied for asylum in the UK, authorities took your fingerprint and added it to the EURODAC database. Italian authorities will check back with that database in case you apply for asylum there and see that you already had a procedure in Great Britain.
You can't have two asylum procedures in two different Dublin III countries. However, if you want to appeal, you can do that in the UK. You will get the chance to provide other reasons that have not been taken into consideration during your initial application yet.
Please keep in mind the comment I posted in your other thread: