You want to explore England at the weekends but hotels, B&Bs and the transport are too expensive to do that as often as you would like to. We like to travel and explore at spring and summer weekends but we also have to keep things affordable.
The Lake District and Wales are great places for a long weekend but both are about 4-5 hrs drive away from us. Travelling by car and staying at campsites are the cheapest way to travel. We usually spend 2-3 nights at the same campsite, that gives us a great base to return to, after a day spent with walking, without having to pack and unpack the tent every day. And its good to know that there is an opportunity to have a shower at the end of the day.
If you are driving, fuel will probably be the biggest cost. However for two people it is likely to be cheaper than trains and a lot more flexible than public transport. When we drive to the Lake District or to Wales and usually need a full and a half tank to complete the journey (it is for there and back and includes the local driving during the weekend) (Petrol: £90)
Camping in Wales or in the Lake District is a lot cheaper than staying in a B&B or hotel. There are plenty of campsites to choose from, and many are located in picturesque places. However nights can be cold, so we always take plenty of layers and extra blankets. It usually costs £21-24 per night for a two of us with a 3-men tent and a car. Some campsites calculate their rates per person and/or per tent and car but it usually works out the same amount. (Camping fees for 3 nights: £63-72)
Once you have the basic equipment, walking, climbing, running and cycling are practically free. We plan some walks for the weekend, before we go.
If you want to have a weekend away on a budget than food doesn`t really have to cost more than it would cost at home. You can prepare food at the campsite. We take some sandwiches, snacks for the first day and then shop in a local supermarket. We make sandwiches for the walks, and stop for picnics. We try to make some very simple dishes in the evenings at the campsite. If we are staying for a long weekend we might have a pub dinner on one of the evenings.
A quick example for a cheap weekend away: We spent the Easter weekend (4 days) in the Brecon Beacons. The trip including absolutely everything (fuel, camping fees, food and one pub dinner), was just under £200 for the two of us. That is only £25 per person per day for everything!