Can I still apply with previous lost passport?
Yes, you can still apply with new passport .
Losing a passport with valid or used visas is obviously a set back for a visa applicant. There is absolutely nothing you can do about it. Certain Schengen Embassies/Consulates require to attach lost passports police report which is very common in Asian countries. Also Embassy/Consulate can ask additional explanation letter with reasons for not providing previous passports along with visa application.
Although Schengen Embassies/Consulates requirements are almost the same, the best answer regarding lost passport would always be available from the relevant Embassy/Consulate in which you are going to apply in UK which is presumably France in your case. The Embassy/Consulate in UK would be able to tell you if you need to provide simply an explanation letter or police report.
Since you have previously been issued Schengen visa 3 times, providing photocopies of last Schengen visas along with your application would always be helpful. Even you are unable to provide your photocopies of your last schengen visas, just truthfully write about your last 3 schengen visits in your application form . Your last 3 schengen visits are stored in VIS(Visa Information System) and Embassy/Consulate can easily retrieve your previous entry and exit from their system.
Will I get Rejected?
This is an opinion based answer, still it is written in all Schengen visas application that
"Compliance with required documents does not necessarily means a visa would be issued"
UPDATE: Embassy of France in London also requires a police report for lost passport.