Hi!
"don't have room for a huge tank in the house"
Well, for starters they should never be kept in tanks or vivariums What you need is a large, open topped "tortoise table" as described in the pet tortoise booklet I linked to earlier.
It's safest to start a hatchling tortoise indoors where temperatures can be controlled and you can watch it more carefully, but YES, as soon as you have established that it is thriving and healthy, then you definitely should keep certain species of tortoise outdoors for the Summertime in the UK. Not only is it possible - it is infinitely preferable, both psychologically and physiologically, to keeping them mainly indoors.
For some great ideas of what you need to provide proper outdoor accommodation for a tortoise, please see: www.tortoisetrust.org/articles/habitatdesign.htm
You need good, solid boundaries, and yes, they really can dig, so it needs to be a deep boundary too - ideally bury chicken wire under the whole enclosure to prevent tunnelling escapes.
You must provide a well drained, sandy/soil area, and not leave them on a damp-holding, lush lawn, otherwise your naturally arid-dwelling tortoise is highly likely to develop shell rot on its plastron (underside).
To allow the tortoise a warm, dry area on cooler or rainy days, most keepers/breeders will have adapted a greenhouse to allow free entry as/when the tortoise chooses, or failing that, a small shed with power (for basking lamps and lighting.)
Obviously in extremes of weather, and for periods when you're preparing for hibernation, OR have just got your tortoise up from hibernation, OR while you over-winter your tortoise if it is not hibernating, then yes, a suitable indoor tortoise-table or indoor pen type habitat is necessary. This will also be needed if the tortoise ever needs closer supervision, for example, in the case of it being treated for a medical condition.
This indoor accommodation will require appropriate heating and lighting. Mercury vapour bulbs are ideal (Megaray brand is the best) as they combine heating and UVB in one basking source, but you do need to make sure that there's enough space around/under the lamp to avoid overheating (of both the tortoise, obviously, and of the accommodation (fire risk!))
If you need information about reputable private breeders in your area (as opposed to the many unscrupulous online dealers and pet stores who are known to sell sick imported tortoises) then please email me. I'm no longer living in the UK, but still have a large number of contacts in the UK tortoise-keeping/breeding community.