To avoid the queues, try using your Westminster Abbey tickets early, during off-peak hours. If you're visiting in July or August, arrive at the opening time, or about 20 minutes before. During the popular summer months, you might arrive to see a long line snaking around the block, and it only gets longer as the morning goes on.
Lunchtime is usually the busiest time of the day (just after the Changing of the Guard at Buckingham Palace). Late afternoons can be calmer, but during busy periods it's good to show up well in advance of the last admittance hour as there might be a long line, which means you won't be allowed to enter in time to explore it all.
Worship takes place every day in the Abbey. There are usually four services daily at 7.30am, 8am, 12.30pm, and 5pm. On Sundays there are six services at 8am, 10am, 11.15am, 3pm, 5.45pm, and 6.30pm.