^^If you go west on Drummond Street and then north on Stanhope St, which turns into Park Village East and then pop over the railway track on mornington st, you can avoid Hampsted road (and the traffic on there).
As for getting from westminster, bit difficult to know what to suggest as I don't know the starting point, but I'm inclined to follow mands' suggestion, straight up regent street and then into the park. You might have to do some extreme filtering.
^^If you go west on Drummond Street and then north on Stanhope St, which turns into Park Village East and then pop over the railway track on mornington st, you can avoid Hampsted road (and the traffic on there).
As for getting from westminster, bit difficult to know what to suggest as I don't know the starting point, but I'm inclined to follow mands' suggestion, straight up regent street and then into the park. You might have to do some extreme filtering.