Always know your min-safe altitude
To go around or not???? There is no correct single answer to your question, it depends where you are on the approach. Always ask you self two things: 1. Where am I? (requires good SA) 2. Where am I safe? (i.e. min safe alt, step down alt, etc.)
Back to your question. As a professional IFR pilot, of course you briefed this eventuality in your approach brief. (it is alway easier to make this decision prior to starting the appoach, that is why it is good to pre-brief loss of glide slope so your crew is clear on the plan of action.)
If you are at or above a step down altitude for the segement of the LOC ONLY approach then either level off or descend to the appropriate altitude and continue with the LOC ONLY. If you are below the level of step down altitude (for the segment being flown) then immediately initiate a climb to a safe altitude. From there you can determine if the approach is still effective and determine the best course of action.
If you have not pre-briefed the loss of glideslope event, then it may be best to just initiate a climb, or level at a safe altitude, and commence the missed approach. But... remember that obstacle clearance for the missed approach segment is predicated on commencing the missed approach AT THE MISSED APPOACH POINT. Ergo it is best to fly the LOC to that point (at a safe altitude) and commence the missed approach from there. Of course if at any time ATC puts you on a vector they are now responsible for your obstacle clearance.
When in doubt go into the missed, re-brief and try it again. Better to be a little late, burn more gas, and bring the aricraft, crew & pax home safe then try to be the hero in the Chief Pilots eyes. The last thing that you should be thinking about after you have had an EQUIPMENT FAILURE is what the Chief Pilot is going to say.