...the short answer is no, there are lots of low cost alternatives.
Cold Frames
When I first started growing from seed I bought this cold frame from Aldi, from memory I think it cost around £40. It served me well for 2 years before I finally took the plunge and acquired a green house.
There's lots of other shapes and sizes of cold frames available from a range of suppliers, the option you chose will come down to your available space, personal taste and, of course, your budget. Both of these low cold frames are from Amazon but you can similar from many online companies.
Zippy greenhouses
If you like the idea of what I call a 'zippy greenhouse' (which essentially is a frame, usually made of steel, with a plastic mesh cover) you'll have lots of choice. They come in all shapes and sizes, from 4-tier shelving through to larger walk-in structures. One word of warning, please make sure you anchor them securely as they're very light and if it's a windy day you might find yourself retrieving your greenhouse from your neighbour's garden.
Poly tunnels
Poly tunnels make a good low-cost option, especially if you have raised beds. Like the zippy greenhouses you just need to make sure that you secure them to the ground/soil to ensure they don't get blown away on a windy day.
Make your own
And for those who enjoy a spot of DIY and are looking for inspiration there's lots of tutorials on YouTube. Would love to see photos of your finished projects.
Please remember...
...whether you're nurturing your seedlings in a greenhouse, cold frame, or polytunnel please ensure that you open the doors/lid of your structure during the day. Your seedlings will need ventilation, if they don't get plenty of fresh air they're likely to suffer from' dampening off' and they wont grow into happy and heathy plants.