Britain had their hands full, but they committed to fighting Germany from all corners of the earth on all fronts. So no, Britain would not be slowed down., they committed to fighting full steam ahead.Do you think Britain would have declared war on Italy if they chose not to enter the war in 1940? Didn't Britain have their hands full with the Battle of Britain? If Italy did not declare war, would they have invaded Albania and Greece?
Italy had to make a choice. Germany needed oil. If Italy did not supply oil, Germany would sack Italy.
If Italy stayed "neutral" and supplied oil to Germany, Britain would consider them an enemy and would invade Libya.
Faced with such choice, Italy joined Germany for own integrity, sovereignty, and Dalmatia. Pretty reasonable.