Based on what you wrote there are several pages in the application of interest. I'll give some screen shots of those pages...
The first is pretty straight-forward, it asks for gender and relationship status.
You can see there's a selection for "Separated" and that would be the right choice given what you wrote.
The next one asks about family in the UK, and since you have a husband, you would select "yes
Since you are still married and not divorced, there's another page of interest...
If you answer "No" and "No" to the questions, you will not have to provide further information. Contrary to what the form says, you will not need your husband's passport details if they are not living with you and not travelling with you.
That answers your question. You can optionally include in the Remarks section how long you have been separated and if the relationship has permanently broken down (those two things are not required, and you don't have to include those statements if you don't want to, but it's part of 'standard ECO curiosity').
Very optionally, you can add if your ex is aware of your plans, sometimes they want to know and other times they don't care; it depends upon the overall impression your application makes and how credible your premise is.
If you are visiting him (or any children) you should include that in the premise section.
They know that people go through phases where things are complicated. They also know that a complicated situation does not necessarily signal an intent to violate our laws, so ifyou just play it naturally, you'll be fine (all other things being equal).