I've bought from Aldi online a few times and have been impressed with their service.
Like you say, they don't stipulate delivery date at time of order but have always seemed to be pretty quick (dispatched the day after ordering and delivered within 2 days) and keep you well informed via email, even giving a tracking link.
I've only really bought cases of good value Bordeaux wines from them so far, but did also try some of their Lot series wines. I'd recommend their Gres de Montpellier, especially at its current £4.99 (half price)
https://www.aldi.co.uk/lot-15-grés-de-montpellier/p/068838022097200