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Not having firm travel plans or proof of accommodation does not absolutely prevent you from getting a visa. In fact, article 14 of the Schengen Visa Code reads:
- When applying for a uniform visa, the applicant shall present:
(a) documents indicating the purpose of the journey;
(b) documents in relation to accommodation, or proof of sufficient means to cover his accommodation;
[…]
This clearly implies that not having booked anything yet but showing you have money to pay for it should be enough. Even that requirement can be waived (e.g. for people who regularly visit the Schengen area and have used visas lawfully before) so it's definitely not formally required to book accommodation for every night in advance. Note that being comfortable with cheap accommodation does not help you with this requirement, each country has its own definition of “sufficient means”. For example, for France it's something like €65 a day.
At the same time, the more credible your plan is and the more details and supporting documentation you can provide, the more likely you are to get your application processed (see the comment below), convince the consulate and get the visa. “I just want to roam freely and don't know when I will come back” will probably invite scrutiny. “I want to see Paris, Rome, Amsterdam, and Berlin, haven't booked my accommodation but have a return ticket to the UK” already sounds much better. A day-by-day itinerary with hotel confirmations would seem even better. See also What does "copy of itinerary" mean when applying for a Schengen visa?
Being a UK resident does not exempt you from any requirement but it does help a little bit here as it shows you have a stable situation to return to and you are not seeking to immigrate illegally in the Schengen area. Same thing if you would own a house, etc.
Incidentally, if you want to visit any of the Schengen countries, you don't have much of a choice, you will need a Schengen visa. Once you have it, there is nothing stopping you from altering your plan, staying a little longer somewhere, changing hotels, adding a country to your tour, etc. Downright lying about where you want to go could in principle be grounds for a cancellation of the visa and denial of entry but in practice you could even go to another country entirely without anyone caring.