Hi there, just wanted to offer you some support as it sounds like you're doing great. I'm so sorry, some of the posters on here are so rude. There does seem to be an issue with this on mumsnet at the moment and it isn't as supportive as it should be. Especially the first replies usually.
I completely understand why your daughter is not walking independently on pavements etc. I live in a suburban area, wide footpaths, woodlands, off-road paths and so of course my children walked these routes without buggies young. I took them to London age 2.5 and 4 and we definitely needed the buggy for the 2.5 year old. He wanted to walk and did lots, but I couldn't relax as the pavements were busy with everyone walking fast. It's not about you being nervous, it's about risk and you weigh it up for the lifestyle you have and environment you're in. Nottingham is a very busy city. You're doing great.
One of my children has learning difficulties. We practised as a game in a park, him running and me saying "stop"or "come back" or traffic lights game emg. "Red" meabt stop. Traffic-free places like national trust, zoos, farms, parks are all great to practise walking (and listening!). Walking holding your hand etc. Also, with busy lives I learned to slow down. My 2.5 year old walked with me every day to nursery, holding my hand (must say, 2 years later he became a rubbish walker when he started school as lost fitness!). It took ages! So again, these kind of things are doable if you have the time. Just it's of praise and making it into a game. I realise I was lucky as didn't work full-time.
But basically, be really proud of yourself. Ignore some of the weirdos on here and sounds like you're a lovely Mummy. Hope you meet some lovely nearby mummys on your trips and then you'll find you just notice what they're doing to copy/ ask them. Best of luck to you!