I am an Indian Citizen living in Italy with/on Resident Permit. Can I travel UK for few days to meet my friends without Visa in this case as UK is part of EU. I have already travelled to Germany & Croatia with my Indian Passport & Resident Permit via Road & Air as well.
No. You are able to travel to Germany and Croatia because Germany is a part of the Schengen area, and Croatia is in the process of joining it, and accepts visas issued by Schengen member states. To travel to the UK you will need to apply for a Standard Visitor Visa, as the UK is not a part of the Schengen area. If in doubt, feel free to check here.
As noted in the comment below, it is important to understand that the European Union and the Schengen agreement are not the same. The EU is a trade and customs union that allows freedom of movement for EU citizens - this still requires a passport, for example, when travelling from the UK to France, which are both in the EU. The Schengen agrement abolishes all internal borders between the member states. You should however carry your passport and Schengen visa/residence permit (as a non-EU citizen) or your national ID card as an EU citizen. As an example, Ireland is an EU member that is not a part of the Schengen area, while Switzerland is, but is not an EU/EEA member.