Hiya welcome aboard!

Your BF will have to do some serious research on this. Visa for you shouldn't be a big problem provided that you fulfil the conditions given and supply all the documents needed plus some more

. Here is couple of links to help you:
http://www.vfs-uk-ph.com/index.aspx
http://www.bia.homeoffice.gov.uk/eucitizens/
http://www.ukvisas.gov.uk/en/
http://www.ukvisas.gov.uk/en/ecg/
Next - your boyfriend as citizen of EEA member state (Hungary) has a right to bring you to UK if he is "present and settled" in UK for a year at least (he apparently is - 3 years in here now).
So you can apply either:
- for a fiancée entry visa - but you will have to pay for it the same fee as UK citizen has to (currently 42.120 PHP)
- or you can marry abroad then he can bring you in UK as a "family member of EEA national" - which is free of charge but you still need to apply at the UK Embassy for "Entry Clearance".
Just be aware that obtaining a visit visa might be sometimes very tricky and it is more like the lottery than anything else.
I'm sure that you can find lot of info on this forum, regarding fiancée visa and documents needed, but I'm not sure as what you need to provide for "Entry Clearance" - try to search the links above and try to ask again.
BTW - why not to tell your BF to join this forum too?

You can do this research together

Hope I've been at least a bit helpful, take care and enjoy...
