Wow, I'm overwhelmed by all the responses. I had a busy day of work and didn't think to check MN until today. I really appreciate everyone who has offered clarification on the bubble situation. I was genuinely confused about it, and not asking for a 'loophole'. I am a 'single parent' as I do not get help from DD's father. However, I'm not a 'single adult', so now see that a support bubble wouldn't be applicable. I may form a childcare bubble with my father if it's needed as my workload increases for my dissertation and part-time job. However, I'll obviously try and avoid it, as DD is in nursery for some hours at the moment.
As for all the responses about my partner. I'm pretty shocked! I feel I must have explained the situation poorly, because I really feel quite lucky to have him. I had DD quite young, (pregnant at 19, gave birth at 20). I was always aware that if I found a partner my age at any point after that, it was unlikely they would be ready to leap into the step-father role immediately. I met my partner just after my DD's 2nd birthday and took things very slowly. They did meet and I tried to do fun things as a three. My OH always made an effort with her but never put pressure on it. We were both understanding that she'd never had to share me and I was desperate to ensure she never felt usurped. As a result, after a year together, she seemed to really enjoy spending time as the three of us.
At the beginning of lockdown, my choice was between enduring the majority of 2020 living completely solo with no family in close proximity. (My father and stepmother live an hour or so away, and my mother is currently in another country). Or my OH could move in with us for at least the duration of lockdown. I decided that I would really struggle to be on my own every day endlessly, so asked him if he could move in. He was living with family so there was no pressure from his side, as he was not alone. He chose to live with me so I wouldn't be alone.
His relationship with DD has thrived, in that they like each other and he will speak to her nicely and play with her occasionally. We have obviously been for 10 million of the same walks as a three too! He works full-time, from home at the moment. I don't understand why there would be an expectation to share the childcare with him? It is ultimately not his responsibility. It is incredibly important that he makes an effort with DD and is always kind/caring towards her but he is not her father and I don't expect him to pretend to be. He helps with all the household chores, does the washing and contributes financially to the food shop etc. However, I think expecting him to step into a stepfather role with equal responsibility at 24, would be absurd. I will always feel DD is ultimately my responsibility and equally would be unhappy if he felt he had any control over how I raised her. We can co-exist happily as a three without playing pretend happy families. Maybe as she gets older and the relationship develops, he will become a father figure to her. However, I don't feel he should HAVE to immediately do that, just because he is in a relationship with me. I am a mother first and foremost BUT after that I am also a multi-faceted person with other interests and passions that make me unique.