estimate cost= Flight Tickets + Accomodation + Local Transportation + misc. (food+others)
For details look up these costs online.
I have been through an identical experience, and know a dozen people with similar experiences, practically speaking, your chances all close none.
Its big step and it requires some investment, you could do initial job market probing through the internet to find out if there are opportunities that meet your qualifications, the expected salary and job requirements, but you have to be in the country at the when applying.
Recruitment process in UK takes some time, an average a month, for big companies (Tier-1 consulting) it averages to 2+/-months and may easily extend to 3+ months plus in companies like IBM.
Phone interviews are for pre-screening, you would usually have a face to face interview after that, before going into an assessment center. Moving from one stage to another would require at least week. So assuming you have one application and that will be successful you need to be traveling twice, staying in hotels for a couple of days overall costs is close to renting a studio for a month.
You dont want to put all your eggs in one basket in a single application, so you typically apply in more than one company and then it would be even harder to arrange you will be have different application at different stages and all would require you to around at different times.
If you go after smaller companies through recruiters which is the common practice as its less competitive for someone entering the UK job market most recruiters would not even consider your CV if you dont have a UK address and phone number.
you would need to arrange an accommodation and finances for at least a month without a job and it may even extend to 3months. You could share an appartment or rent a studio and there are many websites for room sharing, this way you would minimize your expenses until you land job.
Definitely there are exceptions to what I've said but it's better to be safe than sorry and good luck with your search.