Obviously this a question which should be answered by a brief sentence such as the one in your question, but if you are forced to go through an online form and there is no option beyond a mandatory yes/no, then you're going to have to say "no".
The reason employers ask this is so they know whether they need to get involved in the process of visa sponsorship. Some companies are simply not able to manage that; others are unwilling. You're not going to get hired by these companies no matter what you put on the form.
Other companies (like your current employer!) are able to do this. But they need to know that it would be required if they wish to hire you.
Assuming this application form allows you to attach a cover letter, or write an introductory note, put the specifics of your visa situation there, so they don't just get a bare "no, I don't have the right to work in the UK" with no other detail.