Hello rohit,i would like to recommend 2 plans
1)London-Brussels-Frankfurt-Berlin-Prague,you can add ireland prior to london as you mentioned the term 'pocket friendly' i have excluded paris,but i advise you to add paris prior to brussels if you can afford.I do have a alternative-(london-paris-zurich-munich-prague)
2)London-paris-zurich-milan-rome(it's an addition) i won't recommend venice as it has nothing lovely.
LONDON-i don't have to mention it specially,it has everything in it.
FRANKFURT-it is a architectural city,you will be surrounded by forts,churches everywhere
BRUSSELS-royal palace is a place to watch,cultural events and festivals are special attraction
PRAGUE-architecture is prague's special attraction along with it's rich culture.
ZURICH-u have to visit lake of zurich where you can for water games.it's my favourite of all.Climate out there is amazing
For 1 week trip, just stick to one visa- UK visa gives you access to UK, Scotland and most of Ireland. Schengen visa gives you access to rest of the European countries. So combining London with say Paris or Amsterdam means paying for two visas (that's Rs.12000+ gone right there only on visa) which is worthless.
For 1 week, I would suggest you to stick to 3-4 cities max, that way you will be able to explore and enjoy in a pocket-friendly budget. You can refer to this blog for all you need to know - its a long one where I painstakingly put in each and every detail which I wished I knew when i was browsing all over the internet to plan my own trip. Suggest you skip the long intro and read from the paragraph "When and Where" till the end. Then you can go to Part 2 which has a few handy money-saving details. Hopefully you will get all your questions answered. If not, drop your questions here and I will help.