Yes, you CAN afford to travel to England especially if you take advantage of the Hoxton Hotel deal. You can book a room for about $2 a night. Yes, you read that correctly, a boutique hotel in London for ONE pound sterling! This is not a hostel, but a hotel room in a hip stylish hotel that includes a free healthy breakfast (fresh orange juice, yogurt, banana), WiFi, and the rooms come equipped with a duck feather duvet and Aveda products! They try to include thoughtful touches like low international phone rates; calls to the US are only 5p per minute (about 10 cents). There is a limit of only one room per person at this special rate (you can sleep up to 2 people in a room), and to be sure you get a chance to book, you should sign up on their mailing list (1000 rooms were sold in 20 minutes when they had their last sale), but even without this special deal, prices this summer start around 59 pounds ($120 USD); where else in Europe is there a hotel bargain like this these days?
If nothing but Paris will do for you, then book an apartment and live like a native. I rented my apartment this year through Beau Paris which is an apartment owner maintained service (as opposed to a real estate type of management service). There are dozens of pictures and helpful materials about the area that were sent to me before my arrival. I loved my flat with all the thoughtful amenities: a computer with high speed Internet access, a washer and drying rack in the apartment, CD's, books, a flat screen TV, and a welcome bottle of wine. It cost about $120 a night for 3 nights (less if you stay longer) in a one bedroom that slept four comfortably. The owners speak perfect English and they were only a telephone call away for any questions about their Rue Truffaut property (read the posted comments to read more about my impressions of this property).
I was impressed that my rental deposit was returned to my paypal account before my flight landed back in the US, along with an email from the owners thanking me for my stay. I can say that my experience with Beau-Paris was perfect and I would prefer to rent from them than to rent a hotel room any day.
With the high speed train between London and Paris, you can actually visit the two cities if you are staying somewhere else, but it's always better to stay than to visit.